2. SFM Productions Presents: Another exciting episode in your continuing Pre-Calculus experience! 1.8Combinations of Functions: Composite Functions

3. Homework for section 1.8 P8813-27, 37-59, 73

4. Two functions may behave exactly like two numbers in that they may be added, subtracted, multiplied, and divided.

5. Lets say the we have the following functions: f(x) = x+5 g(x) = 3x f(x) + g(x) = ? (f+g)(x) = 4x+5 f(x)  g(x) = ? (f  g)(x) = 3x 2 +15x (f  g)(-5) = ?

6. or a parenthesis? But, do we use a bracket The farthest right we can even think of going on the number line is: The farthest left we can even think of going on the number line is: 02 To find the quotients’ domains, we first have to find the domain of f(x) and g(x) individually. The domain of the quotient is the intersection of the domain of f(x) and g(x).intersection Find the domain of each of these combinations… D: or a parenthesis? But, do we use a bracket [ 0, 2 ) (0, 2 ]

7. It’s important to remember: ANY restriction on functions f and g MUST be considered when forming the: Sum, Difference, Product, or Quotient of f and g.

8. Composition of Functions : just another way to combine functions… If f(x) = x 2 and g(x) = x + 1, then the composition of f with g is: (f o g)(x) - pronounced “the f of the g of x”. (Or as I like to call it: fog x.) (f o g)(x) = f ( g(x) ) = f(x + 1)= (x + 1) 2 * Domain of f o g is all x values in the domain of g where g(x) is in the domain of f. what the heck does that mean????? Do this by working from the inside out…

9. a)find (f o g)(x) b)find the domain of (f o g)(x) Why? The domain of g(x) is [-3,3]. These are the only values you can even think of trying to fit into the domain of (f o g)(x).

10. a)find (f o g)(x) b)find the domain of (f o g)(x) D:

11. Identifying a composite function: it is used in calculus - need to be able to determine which two functions make up the composite function. You must be the function………… This means we must find: f(x) and g(x) such that their composition gives us h(x)… so that: (f o g)(x) =h(x)

13. Go! Do!